B2.8 Multiply and divide fractions by fractions, using tools in various contexts.
Activity 1: Measuring Tapes (Multiplying Fractions and Dividing Fractions by Other Fractions)
Materials
- 1 measuring tape per 2 students
- blank number lines
- fraction strips
Divide the class into teams of 2 students.
To begin, have a discussion regarding the 2 main types of measuring tapes: those with metric measurements and those with imperial measurements. For this activity, students will become familiar with imperial measurements.
Before beginning the warm-up activity and challenges, ensure that students can read the tape (imperial measurements).
- What do you notice?
Here are some starting clues:
Notice 4 types of vertical lines.
Feet: At every 12 inches, you will see an oversized vertical line that marks one foot and the total number of inches at that location on the measuring tape.
Inches: You will see a bold number and a long vertical line at each inch on the measuring tape.
Half-inches: Located between the bolded numbers, you will see a long vertical line that marks the half inch. This long vertical line is not accompanied by a number as is the case with the vertical line marking each inch.
\(\frac{1}{8}\) inches: Located between all the long vertical lines, you will see short lines. These shorter vertical lines mark each \(\frac{1}{8\;^e}\) of an inch.
Warm-Up Activity :
Students become familiar with imperial measurements. Project instructions on the board. Circulate and answer questions as needed.
Directions
- Locate the following numbers on the tape.
- \(\frac{5}{{16}}\;{\rm{of \; inches}}\)
- \(2\frac{3}{4}\) is read as 2 inches and \(\frac{3}{4}\) inches or \(2\frac{3}{4}\) inches
- \(4\frac{1}{2}\)
- \(1\frac{1}{8}\)
- Measure 3 objects located in the classroom and write the length in inches and fractions of an inch. Compare the lengths found with your colleagues. Place importance on the accuracy of the measurements.
Challenges
Emphasize students' strategies. Circulate and take pictures of different solutions. Provide feedback based on the students' solutions and strategies. Students should be able to communicate their solution process mathematically.
Challenge 1:
The activity table at the back takes up \(\frac{1}{{16}}\) the width of the classroom and \(\frac{1}{8}\) the length.
What fraction of the classroom floor area does the activity table occupy?
* Take a desk or some of your tables and adjust the challenge to your needs.
* Check with the real measurements of the table.
Are the measurements necessary to solve this problem?
Challenge 2:
The teacher has cubes measuring \(\frac{7}{8}\) inches to place on a length of 12 inches and \(\frac{1}{4}\). How many cubes does he need?
*Use the measuring tape to help you. Develop a resolution strategy.
*If you have cubes, modify the challenge to your measurements.
Challenge 3:
A long rope is 72 inches and \(\frac{3}{4}\). The physical education teacher wants to have smaller ropes measuring 10 inches and \(\frac{1}{2}\). She therefore cuts the long rope every 10 inches and \(\frac{1}{2}\).
How many pieces will she have? Explain your approach.
* Students will need to get into the habit of estimating their answer before beginning their work.
* Each team can have a different length of rope and do the exercise, changing the length of the small rope as needed.
Activity 2: Community Garden (Operations on Fractions)
Materials
- graph paper
- geometric tiles (other relevant manipulatives)
- coloured pencils
Divide your class into teams of 4 students. Students will be asked to answer a series of questions related to a community garden. Finally, they will have to draw each area of the community garden using graph paper or a drawing program.
Open task (suggestion: give an area that divides by 16)
A community garden of rectangular shape has a total area of ______ square metres. Its length is _______metres.
After consultation, the gardeners divide the garden area. Thus, they reserve \(\frac{3}{8}\) of the total garden area for growing potatoes, \(\frac{1}{8}\) for growing carrots and \(\frac {1}{{16}}\) for growing tomatoes.
- The area set aside for cucumbers is half the size of the area set aside for carrots. What fraction of the garden does this area represent?
- Pumpkins occupy \(\frac{1}{8}\) of the total area. What is the area of this area?
- The rest of the garden will be divided into 2 sections of equal area. One of the section will be reserved for the onions and the other for the peppers. What fraction represents each sector?
- What is the area of each section of the garden?
- Draw the community garden on a grid sheet, colouring each area with different colours.
How might you make sure you have the right solutions?